In this paper we will investigate regularity problem at in infinity for solutions of elliptic equation of second order with respect to mixed Dirichlet and Neumann boundary conditions. We will show that under some assumption on Dirichlet and Neumann parts of the boundary solution is regular at in infinity.

First this type of test was obtained in breakthrough work by Vladimir Mazya for elliptic equations in divergent form in "An analogue of Wiener's criterion for the Zaremba problem in a cylindrical domain." Funktsional. Anal. i Prilozhen. 16 (1982), No. 4.

In the current research both divergent and non-divergent equations will be considered. Main result for divergent equation is part of joint project with Alexander Grigoryan from Bielefield University. The main result for non-divergent equation is joint project with Alexander Nazarov from St. Petersburg Department of V.A.Steklov Institute of Mathematics.